Do they take floppy disks? I know they take the drives but not sure about the disks.

No. At least not willingly. ;)

Magnetic tape media including floppies and vhs tapes and tape carts is about 2c a lb. wholesale!

Best bet is to drop them at a local electronics store in the printer cartridge bin. Same pc-abs plastic and those recyclers are set up for recovery.

Only time they're worth any is if the media is a reddish golden brown. OLD 8 inch disks and ancient tape backups or drum replacement tape kits. Those have copper and gold in the magnetic coating and run about 20c a pound.

Second idea... look in the yellow pages (it's a book they toss in your lawn once a year lol) for a plastics company and see if they will pay for them but don't expect much.
Company in Chicago called ABCP used to buy them for a penny per 10 disks. Another thought for you.